To determine which bag has more fruit, we first need to analyze the ratios of fruit to nuts for each bag and then calculate the actual number of fruit pieces in each.
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First Bag:
- Ratio of fruit to nuts = 3:5
- Let the number of fruit pieces be \(3x\) and the number of nuts be \(5x\).
- The total number of pieces in the first bag is \(3x + 5x = 8x\).
- Since the total is 60, we set up the equation: \(8x = 60\).
- Solving for \(x\) gives \(x = 60 / 8 = 7.5\).
- Now, calculate the number of fruit pieces: \(3x = 3 \times 7.5 = 22.5\).
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Second Bag:
- Ratio of fruit to nuts = 7:10
- Let the number of fruit pieces be \(7y\) and the number of nuts be \(10y\).
- The total number of pieces in the second bag is \(7y + 10y = 17y\).
- Since the total is 60, we set up the equation: \(17y = 60\).
- Solving for \(y\) gives \(y = 60 / 17 \approx 3.53\).
- Now, calculate the number of fruit pieces: \(7y = 7 \times (60 / 17) \approx 24.12\).
Now we can compare the number of fruit pieces in both bags:
- First bag has approximately 22.5 fruit pieces.
- Second bag has approximately 24.12 fruit pieces.
Conclusion: The second bag has more fruit. Thus, the correct statement is:
"The second bag, because the ratio is greater."
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